The current for the (aw) is correct if the problem did not also have a capacitor listed in the components also. listing the problem would help.
The true current for this problem would have to include the the capacitor, making the impedance (Z) = (5 + j5 - j7)

Step 2 of 5

Now current in main winding,
is determined as follows:

Here

Main winding resistance is

Main winding impedance is

Substitute 120 V for
,
for
and
for
as follows:

Now converting both
and
in rectangular form.

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Step 3 of 5

Now the locked–rotor current,
is the sum of
and
.

Substitute
for
and
for
as follows:

Convert the above value into rectangular components as:

Hence, the magnitude and angle of the locked –rotor current is
and
respectively.

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Step 4 of 5

(b) Now the angle between main and auxiliary winding current,
is determined as follows:

Hence, the phase angle between main and auxiliary winding
current is
.

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Step 5 of 5

(c) The maximum starting torque will occur at a phase angle of
. Let
be the angle of current in the auxiliary winding with a capacitor
installed. Therefore we can write the following equation:

Since
is positive then, the current in the auxiliary winding is leading
the voltage as shown in the figure below:

The circuit diagram for split phase induction motor is shown
below:

Figure 1

Phasor diagram for the split phase induction motor is shown as
Figure 2: